Parametric Extended General Mixed Variational Inequalities

Muhammad Aslam Noor

doi:10.1155/2012/201947

Abstract

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational inequalities, quasi (mixed) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results.

Highlights

In recent years, much attention have been given to investigate the behaviour of the changes of the data of the given problems
Since estimating problem data often introduces measurement errors, sensitivity analysis helps in identifying sensitive parameters that should be obtained with relatively high accuracy
Sensitivity analysis may help to predict the future changes of the equilibrium as a result of changes in the governing systems

Summary

Introduction

Much attention have been given to investigate the behaviour of the changes of the data of the given problems. Dafermos 4 used the fixed-point formulation to consider the sensitivity analysis of the classical variational inequalities This technique has been modified and extended by many. We would like to point out that the resolvent equations technique is quite general, unified, and flexible and provides us with a new approach to study the sensitivity analysis of variational inclusions and related optimization problems. We use this alternative equivalent formulation to develop sensitivity analysis for the extended general mixed variational inequalities without assuming the differentiability of the given data. Our results can be considered as significant extensions of the results of Dafermos 4 , Moudafi and Noor 11 , Noor 9 , and others in this area

Preliminaries

Main Results

Conclusion